Fine and hyperfine structure in different bound systems

Abstract

We demonstrate that the generalized Gell-Mann-Low theorem permits for a systematic expansion around the nonrelativistic limit when applied to bound states in the Wick-Cutkosky model, Yukawa theory, and QED (in Coulomb gauge). We apply this expansion to obtain new results for the fine and hyperfine structure of bound states in the cases of the Wick-Cutkosky model and Yukawa theory, and reproduce correctly the fine and hyperfine structure of hydrogenic systems.